Solving Equations with 2 Variables

Each snack costs £2, so $x$ snacks cost $2\times x=2x$ pounds.

Each water costs £1, so $y$ waters cost $1\times y=y$ pounds.

The two costs together come to £20, so the equation is $2x+y=20$.

Each apple costs £3, so x apples cost $3x$. Each orange costs £2, so y oranges cost $2y$.

The two costs are added together and the total spent is £30, so the equation is $3x+2y=30$.

With x pencils at £2 and y erasers at £3, the total spend is $2x+3y=40$.

Buying 5 pencils costs $2\times 5=10$, so £10 is spent and $40-10=30$, leaving £30.

Each eraser costs £3, so $30÷3=10$. You can still afford 10 erasers.

With x pencils at £2 and y erasers at £3, the total spend is $2x+3y=40$.

Buying 8 erasers costs $3\times 8=24$, so £24 is spent and $40-24=16$, leaving £16.

Each pencil costs £2, so $16÷2=8$. You can still afford 8 pencils.

The total cost is $2x+3y$, where x is the number of pencils and y is the number of erasers.

Buying 6 pencils and 3 erasers costs $2\times 6+3\times 3=12+9=21$, so £21 is spent.

Subtracting from the £40 you started with, $40-21=19$, so you have £19 left.

The line shows the equation $2x+3y=40$, where x is the number of pencils at £2 each and y is the number of erasers at £3 each. Every point on the line is a combination that uses the whole £40.

Point P is at $x=5$ and $y=10$. Checking: 5 pencils cost £10, 10 erasers cost £30, and $10+30=40$.

So P means you can buy 5 pencils and 10 erasers, spending exactly £40 with nothing left over.